Assume two nuclear armed countries (say the US and the Soviet Union (USSR)) are locked in a geopolitical competition of high stakes that can be described using a Prisoners Dilemma Game. In particular assume that if both countries choose peace, payoffs are +10. If both choose war pay-offs are -30. If one choose peace and the other war (ie a surprise attack), then the peaceful nation has a pay-off of -50 and the attacker a pay-off of +20. A. Solve for the Nash Equilibrium of this game.
Assume two nuclear armed countries (say the US and the Soviet Union (USSR)) are locked in a geopolitical competition of high stakes that can be described using a Prisoners Dilemma Game. In particular assume that if both countries choose peace, payoffs are +10. If both choose war pay-offs are -30. If one choose peace and the other war (ie a surprise attack), then the peaceful nation has a pay-off of -50 and the attacker a pay-off of +20. A. Solve for the Nash Equilibrium of this game.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![Assume two nuclear armed countries (say the US and the Soviet Union
(USSR)) are locked in a geopolitical competition of high stakes that can be
described using a Prisoners Dilemma Game. In particular assume that if both
countries choose peace, payoffs are +10. If both choose war pay-offs are -30.
If one choose peace and the other war (ie a surprise attack), then the peaceful
nation has a pay-off of -50 and the attacker a pay-off of +20.
A. Solve for the Nash Equilibrium of this game.
B. Now assume that the two countries have a second-strike capacity that
is they retain the ability to retaliate after a surprise attack and inflict serious
damage on the opponent. Such a second-strike capacity might be because the
country possesses a large enough nuclear arsenal including a bomber fleet and
nuclear submarines.
-
Show how to adapt the game of deterrence to account for this second strike
capacity. What has to be true for the payoffs of both countries following the
second strike so as to ensure that there is no nuclear war in the first place?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6c1715e0-e760-470a-b09d-04a60b449079%2F1ccde867-8806-4fee-a576-17cf88109322%2Fk1itdj8u_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Assume two nuclear armed countries (say the US and the Soviet Union
(USSR)) are locked in a geopolitical competition of high stakes that can be
described using a Prisoners Dilemma Game. In particular assume that if both
countries choose peace, payoffs are +10. If both choose war pay-offs are -30.
If one choose peace and the other war (ie a surprise attack), then the peaceful
nation has a pay-off of -50 and the attacker a pay-off of +20.
A. Solve for the Nash Equilibrium of this game.
B. Now assume that the two countries have a second-strike capacity that
is they retain the ability to retaliate after a surprise attack and inflict serious
damage on the opponent. Such a second-strike capacity might be because the
country possesses a large enough nuclear arsenal including a bomber fleet and
nuclear submarines.
-
Show how to adapt the game of deterrence to account for this second strike
capacity. What has to be true for the payoffs of both countries following the
second strike so as to ensure that there is no nuclear war in the first place?
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